In 1995, when I was working at Bill Holland Cycles in Spring Valley, California, customers would often order the bike of their dreams. Most got a custom
Holland titanium frame and titanium handlebar stem, of course. Some went "all the way", adding a titanium bottom bracket, lightweight 3TTT Prima 220 handlebars, Topline cranks, titanium Speedplay pedals, etc.

Most customers loved their new bikes and heaped praise on Holland Cycles. But occasionally a customer would complain that his new bike was more flexible than his old one. The rumor that titanium frames were noodles for stiffness was going around at the time, and as a result we had been bumping up the diameter of the main tubes to get stiffer frames. We thought the frames were pretty stiff. We were wondering how much stiffer we had to make frames to get them stiff enough to satisfy those customers who wanted more.

Because we wanted a scientific answer to the question, I designed a simple non-destructive deflection test to measure the flexibility of frames. That way I could make a numerical comparison of the stiffness of various frame designs.

Test Procedure

The test is a simple one. I used the shop's granite alignment table to anchor each frame by its bottom bracket shell. This holds the frame in a position horizontal to the ground. The frame is supported only by the bottom bracket shell, leaving all other points on the frame (including head tube and rear dropouts) free to move.

To measure front triangle deflection, I slipped a solid steel bar one inch in diameter through the head tube to simulate a front fork. I located the bar on the ID of the head tube by means of closely machined steel cones at each end. The cones held onto the bar with set screws. I hung 47.5 pounds (21.6 kg) on the bar 23 cm below the bottom edge of the head tube. This load on the front triangle is a combination of lateral bending and a little torque between the frame's head tube and the bottom bracket shell. I measured front triangle deflection at the point on the bar where I applied the load. Even though the steel bar weighs a bit too, I measured deflection of the frame due only to the weight of the 47.5 pounds, having zeroed the dial indicator after I installed the 1 inch steel bar.

After removing the bar from the head tube, I measured rear triangle deflection. I installed a Dura-Ace axle set and skewer in the rear dropouts, being careful to tighten the skewer the same for each test. I hung the same 47.5 pound load from the dropouts and measured rear deflection at the point of loading.

What the Test Does and Does Not Do

I believe these two loading cases cover
the kinds of added stress a frame sees in a real-life hard,
out of the saddle effort, such as a standing start, which is
when I believe the rider is most likely to feel a frame's
flex. Finite
Element Analysis performed some
years ago for Trek, as published in Bike Tech [technical newsletter published by Rodale Press], also found
that highest stress occurs in the standing-start scenario.
There may be other stresses on the frame in other scenarios,
such as hard efforts while seated, that place different
stresses on the frame, but I wanted to keep the test simple.
It is for these reasons that I limited the test to the two
types of deflection discussed.

Limiting this test to measuring just
front triangle and rear triangle lateral stiffness means that
the few beam style or other non-diamond frames I tested may
flex in ways that I did not measure. An example of such flex
might be the movement of the top of the rear wheel from side
to side on frames without seatstays, or lateral saddle
movement in the case of beam frames, etc. I ignored any
vertical loads on the frame, as I believe a traditional
diamond frame resists such loads easily due to its truss
design in the vertical plane. (See Bob Bundy's article
"Frame Stiffness" in the rec.bicycles.tech FAQ.

It should also be noted that this test
measures deflection directly, not stiffness, but the two are
related. Stiffness is the mathematical inverse of deflection.
For example, to calculate the stiffness-to-weight ratio of a
given frame, you would first take the inverse of the frame's
total deflection ("one divided by total
deflection") to find a number which represents the
frame's stiffness, then divide that result by the frame
weight. This gives a stiffness-to-weight ratio.

The First Tests

At first I measured a few frames, including some steel frames with various brands and diameters of tubing, and several of Bill Holland's oversized diameter titanium frames with different tubing sizes. Right away, we could tell that the titanium frames Bill was making at the time were consistently stiffer than standard steel frames in the front triangle, and slightly more flexible in the rear triangle. But when we added the front and rear deflections together for each frame, we found that the total stiffness on most of the titanium frames was higher than that of the baseline steel frames. We thought before the test that the frames were stiff, and now we had the numbers to show it. Still, that some customers felt their Holland titanium frames had too much flex puzzled us for a day or so. We wondered how a frame that measured stiffer could feel more flexible to our customers? Then we remembered that no-one rides only the frame. A rider rides a complete bicycle. All those cool, light weight parts that customers chose to complete their new bike were likely contributing to the flex the riders felt, and that was probably making the difference. Nevertheless, my interest was piqued: how do various frames compare in stiffness?

Over a period of about a year, I deflection tested over 100 frames as the opportunity arose. The most flexible one had a total deflection of 0.86 inches (a steel Pinarello with slim Columbus "Air" tubing built in the early eighties). The stiffest one deflected only 0.26 inches (a Cannondale oversized aluminum track frame). I believe this represents about the total range. I don't think we missed any that are much stiffer or much more flexible, though I would have liked to have measured a Vitus 979 or a TVT carbon, both of which have a reputation for flex. Nevertheless, the range of deflection that I found is probably representative of virtually the whole spectrum. For this reason, I no longer perform this test.

Too Stiff?

Is it possible for a frame to be too stiff? It is tempting to write here about ride quality and vertical compliance or resilience, but since my test was designed to evaluate lateral (and a bit of torsional) stiffness only, and not vertical stiffness, I will confine my comments to this: the only drawback I can see to a frame that is infinitely stiff laterally and torsionally is the possibility of excess weight, if stiffness is achieved by overbuilding the frame.

Too Flexible?

Is it possible for a frame to be too flexible? I believe it is. Under a hard effort by the rider, a flexible frame actually allows the wheels to come out of plane with respect to each other. You can see it in any sprint if you can get a view from the front or behind. All frames do this to some extent, but large or powerful riders may prefer a stiffer frame to minimize this effect.

And a too-flexible frame can be hard to handle in some riding situations. For instance, on high-speed descents and in corners, an overly flexible frame can weave around enough to become a handful to keep under control. In other words, flexible frames can be scary! I once read a quote attributed to Andy Hampsten to the effect that the only thing scarier than descending on a TVT frame was climbing without one! A very flexible frame can be disconcerting enough to cause a rider to back off in some situations where a stiffer frame would allow him to keep up speed.

Frame Size Related To Stiffness

All frame builders know that smaller frames are inherently stiffer and larger frames are inherently more flexible. What I found in my testing is that this effect is greater than I thought. Even the lightest tube sets, when made into a small frame, end up nearly the same stiffness as the heaviest tube sets, when made into a large frame! And many frame models, since the model's identity is often defined by a certain tube set, do not make use of the lighter tubes in the small sizes, nor the heavier tubes in the large sizes. This problem is compounded by the larger frame sizes' often carrying the most powerful riders, and thus needing heavier tube sets. In fact, with the exception of oversize welded aluminum frames, even the stiffest tubing used for large frames did not always make up for the increase in flexibility caused by the larger frame size. In the very large sizes (above 61 cm), the frames are almost never stiff enough to satisfy powerful riders. It is a challenge to the designer to make the small frames as light as possible and large frames stiff enough.

The lines on the graph show the
deflection of the different tubesets when built into
different frame sizes. Tubeset lines that lie lower on the
graph are stiffer, while those that lie higher on the graph
are more flexible. PG means plain gauge, and DB means double
butted.

I interpret the data in this chart as
follows:

Generally, larger frames are more
flexible (that's the upper right), and smaller frames
are more flexible (that's the lower left).

Any given tube set, when made into
smaller and larger frame sizes, should plot along a
sloping curve from lower left to upper right, as the
various lines roughly show.

When comparing tube sets, data
that falls to the left and above indicate a stiffer
tube set, while data that fall to the right and below
show a more flexible tube set.

As many have already said, larger
frames are more flexible than smaller frames built from the
same tubing. The graph helps show by how much. I found that
on average, for a constant lateral test load of 47.5 pounds,
a frame shows roughly a 0.013" increase in deflection
for every centimeter increase in seat tube length. That's
about 3% of the average frame's deflection of 0.40".

Discussion

Deflection testing these frames was an eye-opener. We learned that ordinary Holland frames were plenty stiff enough for most people. And while all Hollands remain custom designed with each customer's specific needs in mind, in general we toned down the diameters (and the stiffness) to more reasonable levels for most customers, and saved weight by doing so. We made a more dramatic change in the design of small frames. By using tubes in small frames that are much smaller diameter than before, we save weight, and the frames are still stiff enough to avoid handling problems. On the other hand, we now design large frames using much larger diameter tubing than before to help stiffen up the frames to satisfy the big guys.

How To Read the Chart

"Brand, Model, Material" are the brand, model and material of the frame. For titanium frames, the letters "db" indicate double butted tubing.

"Size" is the frame size in centimeters measured from the center of the bottom bracket to the top of the top tube. Note that since there are several popular methods for measuring frames, this number may not agree with the frame size as declared by the manufacturer.

"Front" is the deflection of the frame's front triangle in inches. A larger number is more flexible, and a smaller number is stiffer.

"Rear" is the deflection of the frame's rear triangle in inches. A larger number is more flexible, and a smaller number is stiffer.

"Total" is the sum of front deflection and rear deflection in inches. A larger number is more flexible, and a smaller number is stiffer.